Computing fractal dimension in supertransient systems directly, rapidly and reliably

¹ Semel Institute for Neuroscience and Human Behavior, University of California Los Angeles, CA 90024, USA
² University of Groningen, Department of Econometrics - P.O. Box 800 NL-9700 AV, Groningen, The Netherlands

Received: 24 June 2006
Accepted: 31 October 2006

Abstract

Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices and they are a common phenomena in dynamical systems. Superlong chaotic transients are caused by the presence of chaotic saddles whose stable sets have fractal dimensions that are close to phase-space dimension. For many physical systems chaotic saddles have a big impact on laboratory measurements, and it is important to compute the dimension of such stable sets including fractal basin boundaries through a direct method. In this work, we present a new method to compute the dimension of stable sets of chaotic saddles directly, rapidly and reliably.